Big Tex - In my experience, sometimes the tranny shifter linkage is not adjusted quite right. Within the shifter is a switch that should make when neutral is selected, sending power to the switch on the tip of the transfer case shifter, eventually unlocking the transfer case solenoid.
With the engine off, main power and ignition switch on, depress the transfer case shifter button and listen for the solenoid on the t-case to click. If it doesn't click, then while depressing the switch on the transfer case shifter, try wiggling the tranny shifter to and froe within the neutral position. If it clicks at either extreme of the neutral position, you can readjust the cable length at the transmission to get the switch to activate closer to the center of the neutral position.
As for the washer on the linkage and the air switch with the roller arm, That engages the front axle when in low range. Many threads on that thing.
